View source for Physics:Electron–positron annihilation

{{Short description|Collision causing gamma ray emission}}
[[File:Annihilation.png|thumb|350px|Naturally occurring electron-positron annihilation as a result of beta plus decay]]
{{Antimatter}}
'''Electron–positron annihilation''' occurs when an [[Physics:Electron|electron]] ({{SubatomicParticle|Electron}}) and a [[Physics:Positron|positron]] ({{SubatomicParticle|Positron}}, the electron's [[Physics:Antiparticle|antiparticle]]) collide. At low energies, the result of the collision is the [[Physics:Annihilation|annihilation]] of the electron and positron, and the creation of energetic [[Physics:Photon|photon]]s:
:{{SubatomicParticle|Electron}}&nbsp;+&nbsp;{{SubatomicParticle|Positron}}&nbsp;→&nbsp;{{SubatomicParticle|Photon}}&nbsp;+&nbsp;{{SubatomicParticle|Photon}}

At high energies, other particles, such as [[Physics:B meson|B meson]]s or the [[Physics:W and Z bosons|W and Z bosons]], can be created. All processes must satisfy a number of [[Physics:Conservation law|conservation law]]s, including:
*[[Physics:Charge conservation|Conservation of electric charge]]. The net [[Physics:Electric charge|charge]] before and after is zero.
*Conservation of [[Physics:Momentum|linear momentum]] and total [[Physics:Energy|energy]]. This forbids the creation of a single photon. However, in [[Physics:Quantum field theory|quantum field theory]] this process is allowed; see [[Physics:Annihilation#Examples|examples of annihilation]].
*Conservation of [[Physics:Angular momentum|angular momentum]].
*Conservation of total (i.e. net) [[Physics:Lepton number|lepton number]], which is the number of leptons (such as the electron) minus the number of antileptons (such as the positron); this can be described as a [[Physics:Matter#Conservation of matter|conservation of (net) matter]] law.

As with any two charged objects, electrons and positrons may also interact with each other without annihilating, in general by [[Physics:Elastic scattering|elastic scattering]].

==Low-energy case==
There are only a very limited set of possibilities for the final state. The most probable is the creation of two or more gamma photons. Conservation of energy and linear momentum forbid the creation of only one photon. (An exception to this rule can occur for tightly bound atomic electrons.<ref>
{{cite journal
 |author1=L. Sodickson |author2=W. Bowman |author3=J. Stephenson |author4=R. Weinstein |year=1970
 |title=Single-Quantum Annihilation of Positrons
 |journal=[[Physics:Physical Review|Physical Review]]
 |volume=124 |issue=6 |pages=1851–1861
 |doi=10.1103/PhysRev.124.1851
|bibcode=1961PhRv..124.1851S}}</ref>) In the most common case, two gamma photons are created, each with [[Physics:Photon energy|energy]] equal to the rest energy of the electron or positron ({{val|.511|ul=MeV}}).<ref>
{{cite journal
 |author=W.B. Atwood, P.F. Michelson, S.Ritz
 |year=2008
 |title=Una Ventana Abierta a los Confines del Universo
 |journal=Investigación y Ciencia
 |volume=377 |pages=24–31
|language=es}}</ref> A convenient [[Astronomy:Frame of reference|frame of reference]] is that in which the system has no net linear momentum before the annihilation; thus, after collision, the gamma photons are emitted in opposite directions. It is also common for three to be created, since in some angular momentum states, this is necessary to conserve [[Physics:C parity|charge parity]].<ref name="griffiths">
{{cite book
 |author=D.J. Griffiths
 |year=1987
 |title=Introduction to Elementary Particles
 |publisher={{wipe|John Wiley & Sons}}
 |isbn=0-471-60386-4
}}</ref> It is also possible to create any larger number of photons, but the probability becomes lower with each additional gamma photon because these more complex processes have lower [[Physics:Probability amplitude|probability amplitude]]s.

Since [[Physics:Neutrino|neutrino]]s also have a smaller mass than electrons, it is also possible – but exceedingly unlikely – for the annihilation to produce one or more neutrino–antineutrino pairs. The probability for such process is on the order of 10000 times less likely than the annihilation into photons. The same would be true for any other particles, which are as light, as long as they share at least one [[Physics:Fundamental interaction|fundamental interaction]] with electrons and no conservation laws forbid it. However, no other such particles are known.

==High-energy case==
If either the electron or positron, or both, have appreciable [[Physics:Kinetic energy|kinetic energies]], other heavier particles can also be produced (such as [[Physics:D meson|D meson]]s or [[Physics:B meson|B meson]]s), since there is enough kinetic energy in the relative velocities to provide the rest energies of those particles. Alternatively, it is possible to produce photons and other light particles, but they will emerge with higher kinetic energies.

At energies near and beyond the mass of the carriers of the [[Physics:Weak interaction|weak force]], the [[Physics:W and Z bosons|W and Z bosons]], the strength of the weak force becomes comparable to the [[Physics:Electromagnetism|electromagnetic]] force.<ref name="griffiths"/> As a result, it becomes much easier to produce particles such as neutrinos that interact only weakly with other matter.

The heaviest particle pairs yet produced by electron–positron annihilation in [[Physics:Particle accelerator|particle accelerator]]s are [[Physics:W boson|{{SubatomicParticle|W boson+}}–{{SubatomicParticle|W boson-}}]] pairs (mass 80.385 GeV/c<sup>2</sup> × 2). The heaviest single-charged particle is the [[Physics:Z boson|Z boson]] (mass 91.188 GeV/c<sup>2</sup>). The driving motivation for constructing the [[Physics:International Linear Collider|International Linear Collider]] is to produce the [[Physics:Higgs boson|Higgs boson]]s (mass 125.09 GeV/c<sup>2</sup>) in this way.{{Citation needed|date=June 2020}}

[[File:Electron Positron Annihilation.png|thumb|Electron/positron annihilation at various energies]]

==Practical uses==
The electron–positron annihilation process is the physical phenomenon relied on as the basis of [[Physics:Positron emission tomography|positron emission tomography]] (PET) and [[Physics:Positron annihilation spectroscopy|positron annihilation spectroscopy]] (PAS). It is also used as a method of measuring the [[Physics:Fermi surface|Fermi surface]] and [[Physics:Band structure|band structure]] in [[Chemistry:Metal|metal]]s by a technique called [[Physics:Angular Correlation of Electron Positron Annihilation Radiation|Angular Correlation of Electron Positron Annihilation Radiation]].
It is also used for nuclear transition.
Positron annihilation spectroscopy is also used for the study of crystallographic defects in metals and semiconductors;
it is considered the only direct probe for vacancy-type defects.<ref>
{{cite journal
 |author=F. Tuomisto and I. Makkonen
 |year=2013
 |title=Defect identification in semiconductors with positron annihilation: Experiment and theory
 |journal=[[Physics:Reviews of Modern Physics|Reviews of Modern Physics]]
 |volume=85 |issue=4
 |pages=1583–1631
 |doi=10.1103/RevModPhys.85.1583
|bibcode=2013RvMP...85.1583T|hdl=10138/306582
 |s2cid=41119818
 |url=https://aaltodoc.aalto.fi/handle/123456789/30859
 |hdl-access=free
 }}</ref>

==Reverse reaction==
The reverse reaction, electron–positron creation, is a form of [[Physics:Pair production|pair production]] governed by [[Physics:Two-photon physics|two-photon physics]].

==See also==
*[[Physics:Bhabha scattering|Bhabha scattering]]
*[[Physics:List of particles|List of particles]]
*[[Physics:Meitner–Hupfeld effect|Meitner–Hupfeld effect]]
*[[Physics:Pair production|Pair production]]
*[[Physics:Positronium|Positronium]]

==References==
{{Reflist}}


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